Решение:
Сторона:
b = √a2 + c2 - 2ac·cos(β°)
= √25.052 + 11.9252 - 2·25.05·11.925·cos(74°)
= √627.5 + 142.21 - 597.44·0.2756
= √605.06
= 24.6
Высота :
hc = a·sin(β°)
= 25.05·sin(74°)
= 25.05·0.9613
= 24.08
Угол:
α° = arcsin(
sin(β°))
= arcsin(
sin(74°))
= arcsin(1.018·0.9613)
= 78.13°
или:
α° = arccos(
)
= arccos(
24.62+11.9252-25.052
2·24.6·11.925
)
= arccos(
605.16+142.205625-627.5025
586.71
)
= 78.21°
Угол:
γ° = arcsin(
sin(α°))
= arcsin(
sin(74°))
= arcsin(0.4848·0.9613)
= 27.78°
Периметр:
P = a + b + c
= 25.05 + 24.6 + 11.925
= 61.58
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√30.79·(30.79-25.05)·(30.79-24.6)·(30.79-11.925)
=√30.79 · 5.74 · 6.19 · 18.865
=√20638.06803751
= 143.66
Высота :
ha =
=
= 11.47
hb =
=
= 11.68